Journal of Fluid Mechanics



Papers

Vortex motion in a weak background shear flow


KONRAD BAJER a1, ANDREW P. BASSOM a2 and ANDREW D. GILBERT a2
a1 Institute of Geophysics, Warsaw University, Poland
a2 Department of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK

Article author query
bajer k   [Google Scholar] 
bassom a   [Google Scholar] 
gilbert a   [Google Scholar] 
 

Abstract

A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale $L$ and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale $L$ and these are confirmed by means of numerical simulations.

(Received October 27 2003)
(Revised March 5 2004)



Metrics